Thank you for your reply. I have received a few other replies off list and
would like to publicly thank all of the people who have offered advice. I
think I have enough information to proceed, I just have to wait to save up
the money :-)

As for the use of a surname as a middle name, I agree that this was commonly
meant to show maternal heritage. However, in the case of illegitimate
children, I know that it was sometimes used to identify the father as well.
This might have been to recognise the father, or might have been to apply
pressure on him for support. Conventional genealogy has not shown this
particular surname in the maternal line. Hence, I take this as a possible
starting point for my quest.

Again, thanks to all who have responded.

Vern

> Vern,
>
> I'm not sure if you got an answer, so I will jump in. Your questions:
>
> 1a. Yes, if you and your second cousin are straight line male descendants
> of the two brothers, a DNA test on you and your second cousin will show if
> the same man was the father of the two brothers.
>
> 1b. It doesn't really matter which generation tests, even if they are of
> two different generations. In cases where I have the opportunity to
> select the generation, I prefer to choose the oldest. This is to reduce
> the very small probability that a mutation happened between father and
> son. So, in your case, I would test you and the son of your second cousin
> if your second cousin did not want to test. If he does, however, I would
> test your second cousin over his son.
>
> 1c. You want to do a Y-DNA test. The Y-chromosome is passed from father
> to son, to his son, to his son, etc. without any changes (except for those
> due to a very slow mutation rate). I recommend the 67-marker test at
> Family Tree DNA as the most comprehensive.
>
> 2. If a surname appears as a middle name, and if it reflects parentage,
> then it is most likely a maternal surname. Your Y-DNA tests reflect your
> paternal heritage, not maternal. While you could check Y-DNA results for
> that surname, they would not match your results. At this time, you need
> to use convention genealogy to determine if that surname is on one of your
> maternal lines.
>
> Yours aye,
>
> Bob McLaren